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Hybrid quantum systems involving cold atoms and microwave resonators can enable cavity-mediated infinite-range interactions between atomic spin systems and realize atomic quantum memories and transducers for microwave to optical conversion. To achieve strong coupling of atoms to on-chip microwave resonators, it was suggested to use atomic Rydberg states with strong electric dipole transitions. Here we report on the realization of coherent coupling of a Rydberg transition of ultracold atoms trapped on an integrated superconducting atom chip to the microwave field of an on-chip coplanar waveguide resonator. We observe and characterize the cavity driven Rabi oscillations between a pair of Rydberg states of atoms in an inhomogeneous electric field near the chip surface. Our studies demonstrate the feasibility, but also reveal the challenges, of coherent state manipulation of Rydberg atoms interacting with superconducting circuits., 12 pages, 4 figures

Magnetic field sensors that exploit quantum effects have shown that they can outperform classical sensors in terms of sensitivity enabling a range of novel applications in future, such as a brain machine interface. Negatively charged nitrogen-vacancy (NV) centers in diamond have emerged as a promising high sensitivity platform for measuring magnetic fields at room temperature. Transferring this technology from laboratory setups into products and applications, the total size of the sensor, the overall power consumption, and the costs need to be reduced and optimized. Here, we demonstrate a fiber-based NV magnetometer featuring a complete integration of all functional components without using any bulky laboratory equipment. This integrated prototype allows portable measurement of magnetic fields with a sensitivity of 344 pT/ SqrtHz.

We report on measurements on the 5S-6P rubidium transition frequencies for rubidium isotopes with an absolute uncertainty of better than \SI{450}{kHz} for the 5S $\rightarrow$ 6P$_{1/2}$ transition and \SI{20}{kHz} for the 5S $\rightarrow$ 6P$_{3/2}$ transition, achieved by saturation absorption spectroscopy. From the results we derive the hyperfine splitting with an accuracy of \SI{460}{kHz} and \SI{30}{kHz}, respectively. We also verify the literature values for the isotope shifts as well as magnetic dipole constant and the electric quadrupole constant., Comment: 7 Figures, 7 pages

In this work, numerical calculations were implemented based on the diagonalisation of a matrix representation of the Stark Hamiltonian on a subset of the basis given by the zero-field Hamiltonian. Dipole matrix elements between the involved states were calculated, which allow for the prediction of transition strengths to Stark shifted Rydberg states. The applicability of the numerical methods were confirmed experimentally by precision spectroscopy in a rubidium vapour cell with electrodes using electromagnetically induced transparency (EIT). The numerical methods were then extended to predict ionisation rates of Rydberg states in the highly Stark shifted regime beyond the classical ionisation threshold. For this purpose, a complex absorbing potential (CAP) was specifically adjusted to the Stark Hamiltonian. An experiment was conducted, in which cold atoms from a magneto-optical trap (MOT) were excited to Stark shifted Rydberg states and the arising ions were detected. The obtained ionisation spectra agree well with the results from the numerical calculations. Another extension of the numerical methods was implemented for crossed electric and magnetic fields. This was used for approximate calculations of the motional Stark effect (MSE), which acts on atoms moving through static magnetic fields and thereby experiencing a Lorentz electric field. In a precision spectroscopy, once more using EIT in a vapour cell, the MSE was observed in low magnetic fields for the first time in rubidium. The spectral shift, which is caused by the MSE, matches the prediction from the numerical calculations. In a final experiment, the practical use of the knowledge of several properties of Stark shifted Rydberg states was illustrated. The numerical methods including the CAP were used to specifically select states for their optical accessibility, permanent electric dipole moments and ionisation rates. In the experiment, atoms from a MOT were excited to these states to observe different characteristics of the dipole blockade effect. The detection scheme for this experiment was realised by controlled ionisation using only small changes in the external electric field., Im Rahmen dieser Arbeit wurden numerische Berechnungen durchgeführt, die auf der Diagonalisierung einer Matrix-Repräsentation des Stark-Hamilton-Operators auf einer Untermenge der Basis, gegeben durch den Null-Feld-Hamilton-Operator, beruhen. Es wurden Dipol-Matrix-Elemente zwischen den beteiligten Zuständen berechnet, die die Vorhersage der Übergangsstärken in Stark-verschobene Zustände ermöglichen. Die Anwendbarkeit der numerischen Methoden wurde experimentell durch Präzisionsspektroskopie in einer Rubidium-Dampfzelle mit Elektroden, unter Ausnutzung von elektromagnetisch induzierter Transparenz (EIT), bestätigt. Die numerischen Methoden wurden erweitert, um die Ionisationsraten von Rydberg-Atomen im weit-Stark-verschobenen Regime, d.h. jenseits der klassischen Ionisationskante, vorherzusagen. Zu diesem Zweck wurde ein "complex absorbing potential" (CAP) speziell an den Stark-Hamilton-Operator angepasst. In einem Experiment wurden kalte Atome aus einer magneto-optischen Falle (engl. "magneto-optical trap", kurz MOT) in Stark-verschobene Rydberg-Zustände angeregt und die entstehenden Ionen anschließend detektiert. Die erhaltenen Ionisationsspektren stimmen mit den Ergebnissen der numerischen Berechnungen gut überein. Daneben wurde eine Erweiterung der numerischen Methoden für gekreuzte elektrische und magnetische Felder implementiert. Dies wurde zur näherungsweisen Berechnung des "motional Stark effect" (MSE) für Atome verwendet, die sich in statischen Magnetfeldern bewegen und dadurch ein Lorentz-elektrisches Feld erfahren. In einer Präzisionsspektroskopie, wiederum unter Verwendung von EIT in einer Dampfzelle, wurde der MSE zum ersten Mal an Rubidium in niedrigen Magnetfeldern beobachtet. Die spektrale Verschiebung, die durch den MSE verursacht wird, stimmt mit der Vorhersage aus den numerischen Berechnungen überein. In einem letzten Experiment wurde der praktische Nutzen der Kenntnis einiger Eigenschaften von Stark-verschobenen Rydberg-Zuständen illustriert. Die numerischen Methoden inklusive des CAPs wurde verwendet, um Zustände speziell nach ihrer optischen Adressierbarkeit, ihren permanenten elektrischen Dipolmomenten und ihren Ionisationsraten auszuwählen. Im zugehörigen Experiment wurden Atome aus einer MOT in diese Zustände angeregt, um die unterschiedlichen Charakteristika des Dipol-Blockade-Effekts zu beobachten. Das Detektionsschema für dieses Experiment wurde durch eine kontrollierte Ionisation mittels kleiner Änderungen des externen elektrischen Feldes realisiert.

We report on the measurement of Stark shifted energy levels of $^{87}$Rb Rydberg atoms in static electric fields by means of electromagnetically induced transparency (EIT). Electric field strengths of up to 500V/cm, ranging beyond the classical ionisation threshold, were applied using electrodes inside a glass cell with rubidium vapour. Stark maps for principal quantum numbers $n=35$ and $n=70$ have been obtained with high signal-to-noise ratio for comparison with results from ab initio calculations following the method described in [M. L. Zimmerman et al., Phys. Rev. A 20, 2251 (1979)], which was originally only verified for states around $n=15$. We also calculate the dipole matrix elements between low-lying states and Stark shifted Rydberg states to give a theoretical estimate of the relative strength of the EIT signal. The present work significantly extends the experimental verification of this numerical method in the range of both high principal quantum numbers and high electric fields with an accuracy of up to 2MHz., 8 pages, 6 figures

We report on a significant discrepancy between recently published highly accurate variational calculations and precise measurements of the spectrum of Rydberg states in $^{87}$Rb on the energy scale of fine splitting. Introducing a modified effective single-electron potential we determine the spectrum of the outermost bound electron from a standard WKB approach. Overall very good agreement with precise spectroscopic data is obtained., 6 pages, 2 figures, 3 tables